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Lógica matemática/ d*(-c*(-a)*(-b)+c*(-(-a)*(-b)))

Expresión d*(-c*(-a)*(-b)+c*(-(-a)*(-b)))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    d∧((c∧(¬b)∧(¬(¬a)))∨((¬a)∧(¬b)∧(¬c)))
    $$d \wedge \left(\left(c \wedge \neg b \wedge \neg \left(\neg a\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right)\right)$$
    Solución detallada
    $$\neg \left(\neg a\right) = a$$
    $$c \wedge \neg b \wedge \neg \left(\neg a\right) = a \wedge c \wedge \neg b$$
    $$\left(c \wedge \neg b \wedge \neg \left(\neg a\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right) = \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)$$
    $$d \wedge \left(\left(c \wedge \neg b \wedge \neg \left(\neg a\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right)\right) = d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)$$
    Simplificación [src]
    $$d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)$$ 
    d∧(¬b)∧(a∨(¬c))∧(c∨(¬a))
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
    FNDP [src]
    $$\left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right)$$ 
    (a∧c∧d∧(¬b))∨(d∧(¬a)∧(¬b)∧(¬c))
    FNC [src]
    Ya está reducido a FNC
    $$d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)$$ 
    d∧(¬b)∧(a∨(¬c))∧(c∨(¬a))
    FNCD [src]
    $$d \wedge \neg b \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right)$$ 
    d∧(¬b)∧(a∨(¬c))∧(c∨(¬a))
    FND [src]
    $$\left(a \wedge c \wedge d \wedge \neg b\right) \vee \left(a \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge d \wedge \neg b \wedge \neg c\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right)$$ 
    (a∧c∧d∧(¬b))∨(a∧d∧(¬a)∧(¬b))∨(c∧d∧(¬b)∧(¬c))∨(d∧(¬a)∧(¬b)∧(¬c))
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